In many applications sophisticated electronics are utilized to automatically solve a complex system of linear equations involving a Hermitian matrix. Generally, real time quadratic optimization problems that arise in linear and nonlinear estimation lead to such a system of equations. Some specific examples of apparatus involving such problems include adaptive antenna array processing, speech processing, spectral estimation, CAT scanning, picture processing, trajectory estimation, etc. For purposes of this disclosure, adaptive antenna array processing systems are disclosed but it should be understood that the disclosed apparatus and processes may be adapted to operate with any of the above described systems.
A complex system of linear equations involving a Hermitian matrix may be solved by means of an approach known as Sample Matrix Inversion (SMI), involving the inversion of the Hermitian matrix. However, this approach is generally extremely complicated and apparatus for mechanizing it is generally complicated and expensive. The present approach, referred to as the Batch Covariance Relaxation (BCR) approach, is much simpler to implement and, if a plurality of BCR modules are used in parallel, i.e., time-multiplexed, or are cascaded, the operating time of the processing may be the same, or even reduced, in comparison to the operating time required in the SMI system.